Characteristic analysis for integrable soliton models on two-dimensional target spaces
arXiv:1503.00641 · doi:10.1063/1.4936147
Abstract
We investigate the evolutionary aspects of some integrable soliton models whose Lagrangians are derived from the pullback of a volume-form to a two-dimensional target space. These models are known to have infinitely many conserved quantities and support various types of exact analytic solutions with nontrivial topology. In particular, we show that, in spite of the fact that they admit nice smooth solutions, wave propagation about these solutions will always be ill-posed. This is related to the fact that the corresponding Euler-Lagrange equations are not of hyperbolic type.
11 pages; v2 minor changes in text, conclusion added, adapted to JMP size constraints, typos corrected, references added, version to appear in J. Math. Phys
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